MIAMI (AP) — Florida's freshman U.S. senator and rising GOP star Marco Rubio is fighting back against allegations he embellished his family's history in saying his parents fled Cuba after Fidel Castro's communist revolution.

Rubio's Senate website says his parents came to America following Castro's 1959 takeover, and he has always publicly identified with the exile community and called himself a son of exiles in campaign commercials. In turn he has maintained a strong and loyal political following within its Miami hub.

But reports Thursday by the St. Petersburg Times and The Washington Post revealed his parents emigrated to the U.S. in 1956, when Cuban dictator Fulgencia Batista was still in power and Fidel Castro had just been released from prison and exiled in Mexico.

Rubio's father was a security guard at a small store when he and his wife left, according to Rubio's staff, and came for economic reasons. Rubio, 40, was born in 1971 in the United States.

Rubio responded to the report with a statement saying his parents had tried to return to Cuba in March of 1961 in hopes that things were improving on the island post-revolution but quickly left because they did not want to live under communism.

"My parents are from Cuba. After arriving in the United States, they had always hoped to one day return to Cuba if things improved and traveled there several times," he wrote. "In 1961, my mother and older siblings did in fact return to Cuba while my father stayed behind wrapping up the family's matters in the U.S. After just a few weeks living there, she fully realized the true nature of the direction Castro was taking Cuba and returned to the United States one month later, never to return."

Rubio's staff said they expected to update his Senate website to reflect the date his parents came to the United States.

The family's effort to return came at a tumultuous time as the U.S. confrontation with Castro's Communists heated up and more than a thousand Cuban exiles from Miami were preparing for their doomed April 1961 Bay of Pigs invasion meant to topple Castro's fledgling government.

As early as January of 1961, U.S. President John F. Kennedy warned in his State of the Union: "Communist agents seeking to exploit that region's peaceful revolution of hope have established a base on Cuba, only 90 miles from our shores."

"You got to remember over 80 percent of Cubans back then supported the revolution, not Fidel but the revolution. We had another dictatorship, Batista. So everyone thought the revolution was going to bring social change," said Professor Andy Gomez, a senior fellow University of Miami's Institute for Cuban & Cuban-American Studies.

The head of the Miami-based Cuban American National Foundation, Pepe Hernandez, himself an exile and longtime opponent of Castro, said the initial departure date was not important.

"There were a number of people who came here during the Batista regime because they were against Batista somehow," he said. "Then they returned to Cuba when Castro came in because they thought now things were going to change, and then after some time they realized this was not going to happen, he said.

"Maybe their case is not exactly the same. They really came here as immigrants, but the second time the reason was that they couldn't live in Cuba under those circumstances. I don't see any difference between his parents and myself and everyone else who came here."